Moss thrives when conditions favor its growth. Too much shade, compacted soil, poor fertility, poor drainage, and low pH all contribute to moss in lawns. If you can correct all (or most) of these problems, you'll have less moss in the lawn. I'd dethatch, then rake up all the dead stolons along with the moss. Reseed any bare areas - April is the best time to reseed. Then put your lawn on a regular feeding schedule, mow frequently, and water as needed. These steps will help the grass grow lush and thick enough to crowd out any moss. We recommend fertilizing in April, June, September, and the first week of December with a 3-1-2 ratio of complete fertilizer (21-7-14 is a good choice). You may want to have the soil tested because it is likely your soil pH is too low. If that proves true, you'll be advised to add lime. Fall is the best time add lime, but anytime is okay. Following the above guidelines for a healthy lawn should greatly reduce the amount of moss you find in your yard.